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Explore this glossary to learn the essential math terms your student needs to succeed.
A
The absolute value tells us how far a number is from zero on the number line.
An acute angle is an angle that measures more than 0° but less than 90°.
Addition is when we put two or more things together.
Algebra is the part of math where we use letters and symbols to represent numbers.
In math, an algorithm is a specific sequence of steps (a method or procedure) we use to solve a problem or perform a calculation.
In geometry, an altitude is a line segment that starts at the vertex (corner) of a shape and goes straight down to the opposite side (or the line containing the opposite side), forming a right angle.
In math, analysis means breaking something complex into smaller parts so we can better understand how it works.
An angle is the shape made when two rays start at the same point and move in different directions.
Area is the amount of space a flat shape covers.
Arithmetic is the branch of mathematics that deals with basic number operations: adding, subtracting, multiplying, and dividing.
The associative property says that in addition and multiplication, you can group numbers in any way and still get the same answer.
A quantity to which an addend is added, that is, the quantity being augmented by an addend.
In math, the average (or mean) is a way to find the “typical” value in a group of numbers.
In math, axes (plural of axis) are the lines we use to build a coordinate system.
In math, an axiom, or axioma, is a basic rule or statement that we accept as true without needing to prove it.
B
A bar graph, or bar chart, is a way to show the relationship between two quantities using bars, where each bar represents a quantity, and the length or height of the bar shows how much it represents.
In geometry, the base is the side or surface of a figure that is used to measure height.
A system of numerical notation that has 2 rather than 10 as a base.
An operation that combines two objects of one type to form another object of the same type.
A binomial is a type of polynomial that has exactly two terms. These two terms are connected by either an addition or a subtraction sign.
C
Calculus is the branch of mathematics that helps us understand how things change.
Cardinal numbers are the counting numbers we use to show quantity.
In math, a chord is a straight line that connects any two points on the circumference of a circle.
A circle is the set of points in a plane that are all the same distance (equidistant) from a given fixed point, called the center.
In math, a class is a group of numbers or objects that share something in common.
A coefficient is the number that multiplies a variable in an algebraic expression.
The commutative property says that in addition and multiplication, you can change the order of the numbers and still get the same answer.
A composite number is a whole number that has more than two factors.
Something formed in the mind, a thought or notion.
In math, congruence means that two shapes are exactly the same in size and shape.
A constant is a number that always stays the same.
In math, the coordinate plane is a two-dimensional surface used to show positions or locations.
In math, coordinates are numbers that help us find the exact location of a point in space.
A rectangular solid with all equal sides.
When a number is cubed, it means that the number is repeated three times in a multiplication.
A cylinder is a three-dimensional (3-D) solid shape with two identical, flat, circular bases that are parallel and connected by a curved surface.
D
In math, data refers to facts, numbers, or information we gather to answer questions or solve problems.
A decimal is a way of writing numbers that can represent parts of a whole—or whole numbers—using a decimal point.
A decimal fraction is a special kind of fraction written in base 10 using a decimal point.
A decimal point is a dot (.) used to separate the whole number part of a number from the fractional part, if there is one.
The denominator is the bottom number in a fraction.
In geometry, a diagonal is a straight line that connects two corners (or vertices) of a shape, but not ones that are next to each other.
The diameter of a circle is the distance across the circle, passing through the center.
In math, a dichotomy is when we split things into two clear groups that don’t overlap.
In math, the difference is the result we get when we subtract one number from another.
A digit is a single number we use to build other numbers. In our number system, we have 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
In geometry, dilation is a transformation that changes the size of a shape but keeps its overall proportions the same.
A dimension is a way of describing how big something or a distance is in space.
A conclusion proved through deductive reasoning.
Direct variation describes a relationship between two variables that change together in a constant way.
The angular position of two points with respect to each other.
To the RIGHT usually denotes a POSITIVE change. To the LEFT usually denotes a NEGATIVE change.
In school and academics, a discipline is a specific area of study or branch of knowledge.
The amount deducted or subtracted from a cost or price.
The distributive property is a math rule that shows how multiplication interacts with addition and subtraction.
A dividend is the number you want to divide. It’s the starting amount—the total that you’re breaking into equal parts.
Division is the process of separating a whole into equal parts. It’s a way of counting how many times one number (the divisor) fits into another (the dividend).
A divisor is the number that tells us how many equal parts we are splitting something into.
E
An oval. The set of points for which the sum of the distances from each point to two fixed points is equal.
An equation is a math sentence that says two things are equal.
Equivalent fractions are fractions that may look different but represent the same part of a whole.
In geometry, the process of changing one configuration into another, including slides, rotations, and reflections.
No left-overs, no variations or fluctuations.
An even number is any whole number that can be divided by 2 with no remainder.
In math, an event is something that can happen when we do a probability experiment, like rolling a die or flipping a coin.
An exponent is a small number written above and to the right of another number (the base).
An expression is a combination of numbers, variables, and operation symbols (like +, –, ×, or ÷) that represents a value.
F
A factor is a number that divides another number evenly, with no remainder.
A family refers to a group of numbers, shapes, or functions that are related to each other by a common rule, pattern, or structure.
Possible to reach or exceed by counting. Having bounds; limited.
A structure consisting of vertices and edges, where the edges indicate a mapping among the vertices.
A transformation, also called a reflection, that produces a mirror image of a geometric figure.
Counting an item a certain number of times based on the amount of another quantity.
A formula is a mathematical equation that expresses the relationship between different variables.
Directed or facing toward the front.
A whole cut into four equal parts. One of the four equal parts. Half of a half.
A fractal is a special kind of shape that looks the same at different scales.
A fraction is a way of showing a part of a whole.
In math and statistics, frequency tells us how many times a value or event occurs.
A function is a special relationship between two sets of numbers where each input value has exactly one output value.
G
Geometry is the part of math that deals with shapes and how we describe the space around us.
The golden ratio, also known as the golden mean and golden section, is a special number that appears in math, nature, and art.
A golden rectangle is a special kind of rectangle where the sides follow the golden ratio.
The golden section is a special way to divide a line into two parts so that the parts are in perfect proportion.
A googol is an incredibly large number, written as a 1 followed by 100 zeros.
A googolplex is one of the largest named numbers in math.
In math, a graph is a visual representation that shows how two or more quantities are related. It helps us see patterns, trends, and comparisons quickly and clearly.
A statement that one quantity is larger in size than another quantity.
The Greatest Common Factor (GCF) is the biggest number that divides evenly into two or more numbers.
One or more of the same thing (1 apple, 9 dogs, 5 inches, 8 things).
H
In geometry, a hexagon is a two-dimensional (2D), closed shape with six straight sides and six angles.
High-dosage tutoring, also called high-frequency and high-impact tutoring, is a special type of tutoring where students get extra help frequently—often several times a week.
In math, something is horizontal when it runs left to right, straight across, like the horizon you see when the sky meets the earth.
The side of a right triangle that is opposite to the right angle. It is always the longest side of a right triangle.
I
The positive solution of the equation x2=−1, i.e., the −1.
The operator that leaves a given operand unchanged.
The identity property is a mathematical rule that says there are certain special numbers, called identity elements, that don’t change the value of another number when used in an operation.
An imaginary number is a number that involves the square root of a negative number, which is something we can’t do using only real numbers.
An improper fraction is a type of fraction that represents a quantity greater than one whole.
To become greater or larger, as in number, amount, or intensity.
A (usually) small addition or increase.
An independent variable is a value we choose or control in a math problem or experiment.
A deductive proof using contradiction or elimination to rule out all cases except the desired conclusion.
Inductive reasoning is when we look at examples or patterns and use them to make a general rule or prediction.
An inequality is a math sentence that shows one value is bigger, smaller, or just not equal to another.
Impossible to reach or exceed by counting. Having no boundaries or limits. Immeasurably large. Larger than any fixed finite quantity.
An immeasurably small amount or quantity.
Infinity describes something – a number or quantity – that goes on forever.
In math, an input is the number or value that we start with in a function or operation.
The operator in a binary operation, the number that is operated on, the independent variable.
An integer is a whole number that can be positive, negative, or zero.
In math, interior means the inside part of a shape or figure.
In math, an intersection is where two or more things meet or overlap.
In math, an interval shows the space or distance between two numbers.
An inverse operation is a math operation that reverses the effect of another operation.
The mathematical property that, for every operation (addition, subtraction, multiplication, division), there is an operator and an operand whose result under the operation is the Identity Element.
Two variable quantities vary inversely if they multiply to a constant product.
An irrational number is a number that cannot be written as a simple fraction, or ratio, of two integers.
An isosceles triangle is a triangle that has two sides that are the same length and two equal angles opposite those sides.
To repeat an algorithm, using the previous output as the next input.
J
When a quantity varies DIRECTLY to another quantity and INDIRECTLY (INVERSELY) to another, it is said to vary JOINTLY with respect to both.
L
A general principle or rule that is assumed or that has been proven to hold between various quantities.
The Law of Sameness is a concept used at Mathnasium to help students understand that in order to combine or compare mathematical quantities, they must belong to the same category.
Least Common Multiple (LCM) description.
In math, legs are the two sides that form the right angle.
The measurement of something along its greatest dimension.
A smaller quantity. The act of “taking away.”
A statement that one quantity is smaller in size than another quantity.
In math, likelihood is used to talk about how certain or uncertain an event is.
The point beyond which something cannot proceed.
In math, a line is a straight path that goes on forever in both directions.
A line plot is a simple way to organize and display data.
A line segment is a part of a line that has two fixed endpoints.
Having only one dimension.
A function with the characteristic that f(x+y)=f(x)+f(y).
Units that measure 1-D quantities.
In math, a locus (plural: loci) is a collection of points that all meet the same rule or condition.
An alternative notation for expressing an exponent.
In math, logic is the process of using clear and careful thinking to figure things out.
M
In math, magnitude means the size or amount of something.
A physical object that is used to teach an abstract idea in mathematics.
Math skills are the tools students use to understand numbers, solve problems, and think logically about math.
Mathematics is the study of numbers, patterns, shapes, and relationships—and how they all work together.
Science, learning, mental discipline, especially, mathematics (L). “That which is learnt.”
The activity of actively doing math (mentally, verbally, visually, kinesthetically, and in writing).
British spelling of “math.”
In math, a matrix is a way to organize numbers or values into rows and columns — kind of like a spreadsheet or a table.
A number that represents the “center” or “trend” of a set of data. The mean, median, and mode are statistical measures of central tendency.
Measurement is the process of finding out how big, long, heavy, or full something is by using standard units.
In math, the median of a data set is the value that falls in the middle of a data set when the numbers are arranged in order from least to greatest.
Mental math involves using number sense and math strategies to solve problems without writing them down.
A meter is a unit of length in the metric system.
A 1,000-year interval of time.
The quantity from which something is being subtracted.
Another name for subtraction.
A mixed number is a number that includes both a whole number and a proper fraction.
In math, the mode is the number that appears the most frequently in a set of numbers.
In math, a model is a representation that helps us understand and solve problems.
A constant factor by which we can change a thing from one name to another (from one system to another).
The one composed of the many. A collective singular for a group of related objects.
A monomial is a type of algebraic expression that consists of only one term.
A greater or additional quantity.
In math, a multiple of a number is what you get when you multiply that number by a whole number.
The multiplicand is the number that is being multiplied in a multiplication problem.
Multiplication is the process of combining equal groups to find a total.
The multiplier is the number that tells how many groups you have in a multiplication problem.
N
In math, a name is how we identify or refer to something.
Natural numbers are the numbers we use when we count things.
A quantity whose value is less than zero.
If p or q is a true statement, and we know p is false, we have “no choice” but to conclude that q is true.
A prefix meaning not, nullifying.
In math, a non-rigid transformation is a transformation that changes the size, shape, or both of a figure.
In statistics, the distribution of data along a bell-shaped curve that reaches its maximum height at the mean.
In math, the word not is used to show that something is false or does not belong to a group.
A number is a way of showing how many or how much of something there is.
A number line is a visual tool that shows numbers in order along a straight, horizontal line.
Number sense is the ability to understand numbers deeply and use them flexibly.
A symbol or mark used to represent a number.
The numerator is the top number in a fraction.
O
In math, an object is any individual item we can count, measure, move, or study.
An obtuse angle is an angle that is larger than a right angle.
An obtuse triangle is a triangle that has one obtuse angle, which is what we call an angle greater than 90° but less than 180°.
An integer that is not divisible by two. Odd numbers have a remainder of one when divided by two.
An odd number is any whole number that cannot be divided evenly by 2.
The ratio of the number of ways to win to the number of ways to lose.
Used to indicate the Aggregate or Whole that includes the Part or Quantity denoted by the preceding word.
A quantity on which an operation is performed.
In math, an operation is a process we use to work with numbers.
In math, an operator is a symbol or rule that tells us to perform a specific action on a number or expression.
Located directly across from something else.
The number with the same absolute value and different sign.
Numbers with the same absolute value and opposite signs. Two numbers whose sum is 0.
One who starts learning late in life. A “late bloomer.”
In math, order tells us how things are arranged.
The order of operations is a set of rules that tells us the correct order to solve different parts of a math problem.
An ordinal number tells us the position or order of something in a list, rather than how many there are.
In math, the origin is the starting point used for reference on graphs and number lines.
A phrase used to tell how many of a given group of things are currently being considered.
In math, an output is the result we get after applying a rule or operation to an input.
The result of a binary operation. The dependent variable.
P
One object composed of two similar things.
A number or other object whose digits (elements) read the same forward and backward.
A U-shaped curve generated by a quadratic equation.
In math, a paradigm is a way of thinking or a model that shows us how something works.
Parallel lines are lines that are in the same flat surface, called a plane, and always stay the same distance apart, which means they never cross or touch, no matter how far they extend.
A parallelogram is a four-sided shape (a quadrilateral) where both pairs of opposite sides are parallel, which means they run side by side and never cross.
In math, a parameter is a value that stays the same within a specific problem or situation but can change in a different situation.
A component of the whole. A fragment, fraction, section, portion, region, a piece broken off.
In a set of numbers, a rule for being able to figure out what number comes next.
A pentagon is a five-sided shape.
In math, the word per means “for each” or “for every.”
A percent (or percentage) is a way to express a part of a whole as a fraction out of 100.
The percent by which a number changes from an original value.
The third power of an integer: 0, 1, 8, 27, 64, 125... are perfect cubes.
A perfect square is a number we get when we multiply an integer by itself.
In math, the perimeter is the total length around the outside of a two-dimensional shape.
In math, a permutation is an arrangement of items in a specific order.
In math, perpendicular lines are lines that intersect (cross) to form a right angle, which measures exactly 90 degrees.
The number of the Golden Ratio.
A lover of knowledge.
Pi (π) is a special number that tells us how the distance around a circle (its circumference) compares to the distance across the circle (its diameter).
The ratio of the circumference of a circle to its diameter.
Place value tells us what each digit in a number means, depending on where it appears.
A symbol in an expression that may be replaced by any element of the set.
A plane is a perfectly flat surface that goes on forever in all directions.
Another name for addition.
A location in space. A point is 0-D. It has no length, width, or depth.
A polygon is a flat (2-D), closed shape made entirely of straight lines.
A polyhedron is a three-dimensional (3D) shape made up entirely of flat polygon faces.
One who has knowledge of many subjects.
A polynomial is a type of algebraic expression made up of terms that are added or subtracted.
A section or quantity within a larger thing, a part of a whole.
A place or location.
A quantity whose value is greater than zero.
A power is the result of multiplying a number by itself a certain number of times.
A factor of a given number that is itself prime.
A number that has exactly two distinct factors, namely, 1 and itself.
Two prime numbers that differ by 2. 11 and 13 are prime twins, as are 59 and 61.
A prism is a 3-D (three-dimensional) shape with two matching bases that are flat, equal in size, and parallel.
Probability is a way of measuring how likely something is to happen.
A product is the result you get when you multiply two or more numbers together.
In math, a proof is a step-by-step explanation that shows why something is always true, not just for one example, but for all possible cases.
A proper fraction is a fraction that is less than one whole.
In math, a proportion is a statement that two ratios are equal.
In math, we say two things are proportional when they increase or decrease at the same rate.
Reasoning in groups.
A semicircular instrument for measuring and constructing angles.
A pyramid is a three-dimensional (3-D) shape that has a flat base (a polygon) and triangular faces that connect at a single point called the apex.
The Pythagorean Theorem, or Pythagoras' Theorem, is a rule in geometry that helps us find the lengths of sides in a right triangle.
A Pythagorean triple is a set of three whole numbers, usually denoted by a, b, and c, that fit the Pythagorean Theorem.
Q
A function that has an equation of the form y = ax\(^2\) + bx + c where a does not equal 0.
A quadrilateral is any shape that has four straight sides and four angles.
A single term or collection of terms and operators considered as a single entity.
One of four equal parts. Half of a half.
A quotient is the result you get when you divide one number by another.
R
A radian is a way to measure angles, just like degrees, but using a different unit.
In a circle, the radius is the distance from the center of the circle to any point on its circumference.
In math, random means something happens without a set pattern or predictable outcome.
A quantity that is unpredictable.
The range is the set of all the possible values of the dependent variable.
Describes how much one variable changes in relation to another.
A ratio is a way of comparing two quantities.
A rational number is any number that can be written as a fraction or ratio of two integers.
A straight line extending from a point.
A real number is any number you can find on the number line.
A reciprocal is what you multiply a number by to get 1.
A quadrilateral with four right angles.
An organized arrangement of square units (example tiles).
A rectangular prism or cuboid is a three-dimensional (3-D) solid shape with six rectangular faces.
A prism with a rectangular base. A box.
In finite math, a value in a series derived by applying a formula to the previous value.
In finite math, a series of numbers in which values are derived by applying a formula to the previous value.
The mirror image of an object.
A relation is reflexive if each element, a, bears that relation to itself.
A large, usually continuous, segment of a surface or space.
Having equal sides and equal angles.
Any ordered pair of numbers.
In math, a relationship describes how two or more things are connected.
Two or more numbers that have no common factors other than 1. The numbers themselves may or may not be prime, but they are said to be prime, relative to each other.
A remainder is the amount left over when a number cannot be divided evenly.
Turned backward in position, direction, or order.
A rhombus is a four-sided, two-dimensional shape (a quadrilateral) where all four sides are the same length.
An angle whose measure is 90°. Right angles are formed by the perpendicular intersection of two straight lines.
In math, a rigid transformation is a way of moving a shape without stretching or shrinking it.
Roman numerals are a number system that uses letters instead of digits to represent values.
In geometry, a rotation is a type of transformation that turns a shape around a fixed point.
The process of expressing a number to the nearest specified place within a given number system (usually base 10).
A series of objects placed next to each other, usually in a straight line.
A standard method or procedure for solving a class of problems.
S
Similar in kind, quality, quantity, or degree.
In math, particularly in statistics, a sample is a smaller group we choose from a larger group, called the population.
In math, scale describes how we shrink or enlarge something while keeping its shape and proportions the same.
A scale factor tells us how much a figure has been enlarged or reduced.
A scalene triangle is a triangle where all three sides are different lengths, and all three angles are different sizes.
A graph of the points representing a collection of data.
Scientific notation helps us write really big or really small numbers in a shorter, easier way.
A group of 20 items.
In math, a section is one part of something that has been divided into multiple pieces.
The portion of a circle bounded by two radii and the included arc.
A part of a line with a definite beginning and definite end.
In math, a sequence is a list of numbers arranged in a specific order.
A number of objects arranged in a definable order.
In math, a set is a collection of objects, numbers, or things that belong together in a group.
In geometry, a side is one of the straight edges that form the boundary of a shape.
A symbol (+ or –) that indicates whether a quantity is positive or negative.
Same shape, different size.
Containing variables for which there are values that can satisfy all the equations at the same time.
A trigonometric function that is defined as the ratio of the leg opposite the angle to the hypotenuse of a right triangle.
In math, the word “single” means “one,” or not grouped with any others.
Straight lines in space that are neither parallel nor intersecting.
Proficiency that is developed through training and experience.
Counting by equal intervals.
A slide is one of the ways we can move shapes around without changing how they look.
A deviation from the horizontal. An inclined line.
The Socratic method is a way of teaching that helps students learn by asking them questions instead of giving them answers.
The answer to a problem, especially an equation.
In math, space is the environment where mathematical objects, like points, lines, shapes, and figures, exist and interact.
In math and science, speed tells us how fast something is moving.
A sphere is a perfectly round 3-D shape where every point on the surface is the same distance from the center.
A square is a flat shape (polygon) that has four equal sides and four equal angles.
In math, a square root is a number that, when multiplied by itself, gives the original number.
The units used to measure area.
When a number is squared, it means the number is multiplied by itself.
Standard deviation tells us how spread out a set of numbers is.
Having a sharp inclination or slope.
A table utilizing digit(s) of a number as stems and the other plot digit(s) as leaves.
Extending continuously in the same direction without curving.
An angle whose measure is equal to 180°.
Something made up of a number of parts or objects that are held together by a set of rules.
The act of replacing a quantity with an equal quantity.
Subtraction is the process of taking one number away from another.
The quantity that is subtracted from another quantity.
A sum is the result you get when you add two or more numbers together.
The boundary of a 3-D figure. A portion of space having length and breadth but no thickness.
The sum of the areas of all the faces, including the bases, of a 3-D object.
In math, a survey is a way we gather information by asking questions or collecting responses from people.
A relation is symmetric if, for any two elements a and b, the positions of a and b can be switched and the relation remains true.
In math, symmetry means that one part of a figure is a mirror image of another part.
The combining of separate elements to form a coherent whole, the complex whole so formed.
A group of interacting elements forming a complex whole.
T
An informal word for the process of subtraction.
A trigonometric function of an angle which is defined as the ratio of the lengths of the leg opposite to the leg adjacent to an angle in a right triangle.
A mosaic formed by repetitions of a single shape.
A term is a part of a math expression or equation, separated by addition or subtraction signs.
Mathnasium’s proprietary teaching approach designed to help students of all skill levels unlock their math potential.
The metric system is a system of measurement used by most of the world.
The Percent Equation states: Percentage Rate × [Whole] = [Part].
An individual object. An entity thought to have its own existence. A thought, a notion, or an utterance.
A whole cut into three equal parts. One of the three equal parts.
A three-dimensional (3D) shape is a solid object that takes up space.
An interval separating two points on the continuum from yesterday, through today, and into tomorrow.
Another word for the process of multiplication.
In math, a transformation, also called a geometric transformation, is a way to move or change a shape while keeping its structure the same.
The transitive property is a rule in math that helps us understand how things are connected.
A line that intersects a system of other lines, usually parallel lines.
In the US, we define a trapezoid as a four-sided shape (called a quadrilateral) that has exactly one pair of parallel sides.
A triangle is a flat shape (polygon) with three straight sides and three angles.
The property that, for any two given numbers A and B, one and only one of the following relationships is true: Either A=B, A>B, or A
Trigonometry is a branch of mathematics that focuses on triangles, especially right triangles, and the relationships between their angles and sides.
A trinomial is a type of polynomial that has exactly three terms.
Composed of three like parts. Three times as many or as much.
In math, “twice” means “two times as much” or multiplied by 2.
A two-dimensional (2D) shape is flat because it only has two dimensions: length and width.
U
The act of uniting into a new whole.
An individual, a group, a structure, or other entity regarded as an elementary structural or functional constituent of a whole.
A fraction whose numerator is one.
In math, unity is another word for the number 1.
All things, regarded as a whole.
A quantity whose numerical value is not stated.
V
An argument that is correctly inferred or deduced from a premise.
A variable is a symbol, usually a letter, that stands for a number we don’t know yet.
A vector is a quantity that has both direction and magnitude (size).
A vertex is a point where two lines, rays, or sides meet — like a corner.
In math, vertical means straight up and down.
The horizontal bar in a fraction separating the numerator from the denominator. A grouping symbol.
In math, a void is often used informally to describe something that has no quantity, no value, or no content.
In math, volume measures the amount of space within a 3-D object like a box, a ball, or a cylinder.
W
A measure of the heaviness of an object.
Undivided. The one composed of the many. That which can be broken down into parts. All of the quantity under consideration.
A whole number is any positive integer without a fractional or decimal part.
The measurement of the distance of something from side to side.
Z
Zero is the number that means none or nothing.
An angle whose measure equals 0°.
An unspecified, very large, finite number.
